Practical 0.385-Approximation for Submodular Maximization Subject to a Cardinality Constraint

Non-monotone constrained submodular maximization plays a crucial role in various machine learning applications. However, existing algorithms often struggle with a trade-off between approximation guarantees and practical efficiency. The current state-of-the-art is a recent 0.401-approximation algorithm, but its computational complexity makes it highly impractical. The best practical algorithms for the problem only guarantee 1/e-approximation. In this work, we present a novel algorithm for submodular maximization subject to a cardinality constraint that combines a guarantee of 0.385-approximation with a low and practical query complexity of O(n+k²), where n is the size of the ground set and k is the maximum size of a feasible solution. Furthermore, we evaluate the empirical performance of our algorithm in experiments based on the machine learning applications of Movie Recommendation, Image Summarization, and Revenue Maximization. These experiments demonstrate the efficacy of our approach.